Iran’s new president, Hassan Rouhani, is directing overtures of peace toward the Obama administration, suggesting the Iranians would be willing to talk about curtailing its nuclear weapons program in exchange for the end of damaging economic sanctions. It could be one of the most important diplomatic breakthroughs of the Obama presidency.

Hostility from Iran has been a fact of life in U.S. foreign affairs for more than three decades. With the development of its nuclear weapons program and its outspoken hostility toward Israel, Iran was a threat that could not be ignored. Iranian support for the Hezbollah militia in Lebanon and for Syrian President Bashar Assad has involved Iran in the region’s bitterest rivalries.

In the early days of his first term, President Obama let Iran know he was willing to move beyond old animosities. But the repressive response of the Iranian government to a popular uprising following the election of 2009 made rapprochement with the United States impossible.

Recently, the departure of the toxic former president, Mahmoud Ahmadinejad, combined with the economic devastation wrought by international sanctions, seems to have changed the thinking of Iran’s leaders. If they are sincere in their professed desire to resolve their disputes with the West, then Obama and other Western leaders ought to follow up on the Iranian overtures.

Consider the politics of the region as they exist today. The Syrian civil war threatens to plunge the Middle East into a sectarian bloodbath. The rivalry between Sunni and Shia sects is ripping Syria apart, as it did Iraq. Assad is aligned with the Shia, which means he retains the support of Shia Iran and Hezbollah, the Shia sect in Lebanon. Meanwhile, the Sunni monarchies in Saudi Arabia and elsewhere in the Gulf are funding the Syrian rebel opposition.

Because the United States has been aligned against Shia Iran, it has been forced into reliance on Saudi Arabia, a repressive, conservative regime that has been funding Islamist fighters arrayed against the United States. Peace with Iran would free the United States from its dependency on Saudi Arabia. Further, if Iran saw that its interests were served by peace with the United States, it might conclude that it has less to gain from causing trouble for Israel by supporting Hezbollah and Syria.

A peaceful, prosperous Iran would be in the interest of everyone. Reports from Iran suggest that the Iranian people, apart from the religious fanatics, view the United States with extreme favor. Iran is one of the most westernized nations of the region with great commercial potential. Rather than acting as a source of trouble, a peaceful Iran could be a source of stability.

Diplomatic overtures from former enemies always invite suspicion. The offer by Syria to get rid of its chemical weapons has been greeted with skepticism. Iranian offers to talk will have to be tested skillfully. In both cases, leaders may be attempting to string the United States along. But fear of being played for a fool should not be allowed to stand in the way of a breakthrough that could achieve a historic transformation.

It’s impossible to know the behind-the-scenes maneuvering and motivations that drive the conduct of diplomacy. There are those who say that Obama’s threatened strike against Syria has shown that the United States is serious about weapons of mass destruction, including nuclear weapons in Iran. Others say that Obama’s threat was undermined by the reluctance of Congress and the American people to support him.

Whatever is pushing these potential changes, the United States must not miss the opportunity to end the stranglehold that conservative Sunni kingdoms have long had on American foreign policy. A strong, peaceful, prosperous Iran could be an effective counterweight against the forces of extremism. It will be important for Iran to persuade the Obama administration that Iran itself has abandoned extremism. If it has, then dominoes of peace may fall throughout the regime.